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Voiceover
Now let's return to the Diels-Alder reaction, focusing on the carbon atom frameworks. The rearrangements of electron pairs between carbon atoms is often represented by an arrow pushing diagram. As the reaction proceeds, these electron pairs are shifted, as drawn here, in a clockwise direction.

The arrows and electron pairs can just as well be drawn circulating in a counterclockwise direction. Although arrow diagrams and chemical structure formulas are drawn as flat two-dimensional figures on the pages of a book, the atomic nuclei are actually moving in three dimensions throughout the reaction.

Here is the starting ethylene molecule, and here is the starting butadiene molecule separated by a large distance. Single and double bonds are gradually shifting and reforming throughout the reaction.

Now let's look at these electron-pair rearrangements from an orbital viewpoint. The three key electron pair orbitals of the starting reagents are the pi bonds of the butadiene and the pi bond of the ethylene. If we represent the electronic rearrangements in terms of the three filled localized molecular orbitals, the bond shifts appear similar to the arrow pushing diagrams seen before.

However we could just as well picture the orbitals as shifting in a counterclockwise direction rather than clockwise.